Weight adjusted composite model for forecasting in anomalous environments

ABSTRACT

A method, system, and computer program product for weight adjusted composite model for forecasting in anomalous environments are provided in the illustrative embodiments. A base forecasting model and a second forecasting model are combined to form a composite model, the base forecasting model configured to forecast an event in a time series, the second forecasting model configured to represent an anomalous portion of data in the time series. A mixing algorithm is combined with the composite model to adjust a set of weights associated with the composite model. Upon identifying a future period in which the event is to be forecasted, using the mixing algorithm, a subset of the set of weights is adjusted to from a weight adjusted composite model. The weight adjusted composite model is executed to forecast the event in the future period.

TECHNICAL FIELD

The present invention relates generally to a method, system, andcomputer program product for forecasting future events. Moreparticularly, the present invention relates to a method, system, andcomputer program product for weight adjusted composite model forforecasting in anomalous environments.

BACKGROUND

A predictive model (forecasting model, autoregressive model) is asoftware-implemented model of a system, process, or phenomenon, usableto forecast a value, output, or outcome expected from the system,process, or phenomenon. The system, process, or phenomenon that ismodeled is collectively and interchangeably referred to hereinafter as a“process” unless specifically distinguished where used.

A simulation is a method of computationally looking ahead in the futureof the execution of the process to predict one or more events that canbe expected to occur in the process at that future time. A predictedevent is a value, output, or outcome of the process at the end of alook-ahead period configured in the simulation.

A variable that affects an outcome of a process is called a factor or afeature. A predicted event or an outcome of a process is dependent upon,affected by, or otherwise influenced by a set of one or more factors. Afactor can be independent, to wit, independent of and not affected byother factors participating in a given model. A factor can be dependentupon a combination of one or more other independent or dependentfactors.

A predictive model has to be trained before the model can reliablypredict an event in the future of the process with a specified degree ofprobability or confidence. Usually, but not necessarily, the trainingdata includes past or historical outcomes of the process. The trainingprocess adjusts a set of one or more parameters of the model.

Data emitted by a data source is also called a time series. Instatistics, signal processing, and many other fields, a time series is asequence of data points, measured typically at successive times, spacedaccording to uniform time intervals, other periodicity, or othertriggers.

Time series analysis is a method of analyzing time series, for exampleto understand the underlying context of the data points, such as wherethey came from or what generated them. As another example, time seriesanalysis may analyze a time series to make forecasts or predictions.Time series forecasting is the use of a model to forecast future eventsbased on known past events, to wit, to forecast future data pointsbefore they are measured. An example in econometrics is the openingprice of a share of stock based on the stock's past performance, whichuses time series forecasting analytics.

Time series forecasting uses one or more forecasting models to regresson independent factors to produce a dependent factor. For example, ifTiger Woods has been playing golf very quickly, the speed of play is anexample of an independent factor. A forecasting model regresses onhistorical data to predict the future play rates. The future play rateis a dependent factor.

The illustrative embodiments recognize that time series data is notalways uniformly distributed, and includes anomalies. For example, ifthe data pertains to a golfing tournament, the events that occur in thetournament are reflected in the data. The type, spacing, peaking,repetition rate, intensity, duration, and other characteristics of theevents are dependent on a variety of factors, and are thereforenon-uniformly distributed in the data.

The non-uniformity of the distribution of an event in time series datais referred to herein as an anomaly. For example, that an event in theexample golfing data will have a certain value is dependent upon a timeof day when that event is occurring, the slope of the course, a weathercondition at the time, a skill level of the player, and many otherfactors that introduce anomalies in the event's data. For example, theevent may occur more regularly during midday as compared to evenings; orthe event may occur more predictably if a skilled player is playing ascompared to when a novice is playing; and so on.

The illustrative embodiments recognize that presently availableforecasting models are good at forecasting events when they areuniformly distributed in a time series but are often inaccurate whenforecasting those events in anomalous data. Anomalous data is timeseries data that includes one or more anomalies.

The illustrative embodiments further recognize that not only does ananomaly disturb the uniformity of a given time series data, an anomalousportion of that data itself has variability. In other words, theillustrative embodiments recognize that to forecast an event during ananomalous portion of a future time series, one has to also know whichsegment of that future portion is being forecasted.

For example, suppose that training data shows that an anomaly causes anevent to occur with a linearly increasing value from 8 to 32 during ananomalous period of three hours from noon until 3 PM during an otherwiseuniform time series for the remainder of twenty one hours. If the eventis to be forecasted during a day next week, to accurately forecast theevent during 2-3 PM, one has to know the anomalous behavior of the eventnot only between noon and 3 PM, but particularly during the 2-3 PMsegment of that anomalous period because the anomalous values of theevent are different within different segments of the anomalous period aswell.

The linear anomaly is described only as a simplified example ofanomalous data. The illustrative embodiments recognize that the anomalyin the data can be far more complex, such that a polynomial equation inn-degree is needed to suitably model the anomaly curve. In such cases,not only is the polynomial representation of the anomaly important, buthow that polynomial expression changes in different segments of theanomaly curve is important as well.

The illustrative embodiments have already recognized that presentlyavailable forecasting models are inaccurate when forecasting events inanomalous data. The illustrative embodiments further recognize thatforecasting events in specific segments of anomalous data is even morechallenging, and unavailable in presently available forecasting models.

SUMMARY

The illustrative embodiments provide a method, system, and computerprogram product for motion pattern based event detection using awearable device. An embodiment includes a method for event forecastingin anomalous environments. The embodiment combines with a baseforecasting model a second forecasting model to form a composite model,the base forecasting model configured to forecast an event in a timeseries, the second forecasting model configured to represent ananomalous portion of data in the time series. The embodiment combineswith the composite model a mixing algorithm, the mixing algorithmconfigured to adjust a set of weights associated with the compositemodel. The embodiment adjusts, responsive to identifying a future periodin which the event is to be forecasted, using the mixing algorithm, asubset of the set of weights to from a weight adjusted composite model.The embodiment executes, using a processor and a memory, the weightadjusted composite model to forecast the event in the future period.Thus, where the prior-art fails to recognize and act upon anomalies intime series data, the embodiment recognizes the anomalies, and providesa methodology that produces more accurate forecasts as compared to theprior-art in such anomalous environments.

Another embodiment further identifies a characteristic of the futureperiod. The embodiment identifies a second period in a training data,wherein the characteristic of the future period matches a correspondingcharacteristic of the second period within a threshold. The embodimentdetermines a portion of a curve representing a set of anomalous valuesin the training data during the second period, wherein the adjustingmatches a curve representing the composite model during the futureperiod with the portion of the curve representing the set of anomalousvalues in the training data during the second period. Thus, where theprior-art fails to recognize and act upon anomalies in time series data,the embodiment recognizes the anomalies during certain periods, andprovides a methodology that produces more accurate forecasts duringthose periods or portions thereof, as compared to the prior-art in suchanomalous environments.

In another embodiment, the training data comprises past data of the timeseries. Thus the embodiment can be trained to produce event forecasts inanomalous data environments.

In another embodiment the characteristic comprises a factor that affectsthe event during the future period. Thus the embodiment can beconfigured to account for various factors that affect event forecastingin anomalous data environments.

In another embodiment the characteristic comprises a time of day. Thusthe embodiment can be configured to account for a time-related factorthat affects event forecasting in anomalous data environments.

In another embodiment the second forecasting model comprises an equationwhose curve fits, within a threshold, a curve formed by a set of valuesin the anomalous portion, and wherein the base forecasting modelforecasts a value of the event in a non-anomalous portion of the data ofthe time series. Thus the embodiment can be configured to produceaccurate event forecasting during anomalous and non-anomalous periods ina given environment.

Another embodiment further configures the set of weights in thecomposite model, wherein a weight in the set of weights is associatedwith an expression in an equation in the composite model, whereinadjusting the weight causes a curve of the equation to change and form achanged curve, and wherein the changed fits, within a threshold, asecond curve formed by a set of values in an expected anomalous portionin the time series during the future period.

Another embodiment includes a computer program product for eventforecasting in anomalous environments. The embodiment further includesone or more computer-readable tangible storage devices. The embodimentfurther includes program instructions, stored on at least one of the oneor more storage devices, to combine with a base forecasting model asecond forecasting model to form a composite model, the base forecastingmodel configured to forecast an event in a time series, the secondforecasting model configured to represent an anomalous portion of datain the time series. The embodiment further includes programinstructions, stored on at least one of the one or more storage devices,to combine with the composite model a mixing algorithm, the mixingalgorithm configured to adjust a set of weights associated with thecomposite model. The embodiment further includes program instructions,stored on at least one of the one or more storage devices, to adjust,responsive to identifying a future period in which the event is to beforecasted, using the mixing algorithm, a subset of the set of weightsto from a weight adjusted composite model. The embodiment furtherincludes program instructions, stored on at least one of the one or morestorage devices, to execute, using a processor and a memory, the weightadjusted composite model to forecast the event in the future period.Thus, where the prior-art fails to recognize and act upon anomalies intime series data, the embodiment recognizes the anomalies, and providesa methodology that produces more accurate forecasts as compared to theprior-art in such anomalous environments.

Another embodiment includes a computer system for event forecasting inanomalous environments. The embodiment further includes one or moreprocessors, one or more computer-readable memories and one or morecomputer-readable storage devices. The embodiment further includesprogram instructions, stored on at least one of the one or more storagedevices for execution by at least one of the one or more processors viaat least one of the one or more memories, to combine with a baseforecasting model a second forecasting model to form a composite model,the base forecasting model configured to forecast an event in a timeseries, the second forecasting model configured to represent ananomalous portion of data in the time series. The embodiment furtherincludes program instructions, stored on at least one of the one or morestorage devices for execution by at least one of the one or moreprocessors via at least one of the one or more memories, to combine withthe composite model a mixing algorithm, the mixing algorithm configuredto adjust a set of weights associated with the composite model. Theembodiment further includes program instructions, stored on at least oneof the one or more storage devices for execution by at least one of theone or more processors via at least one of the one or more memories, toadjust, responsive to identifying a future period in which the event isto be forecasted, using the mixing algorithm, a subset of the set ofweights to from a weight adjusted composite model. The embodimentfurther includes program instructions, stored on at least one of the oneor more storage devices for execution by at least one of the one or moreprocessors via at least one of the one or more memories, to execute,using a processor and a memory, the weight adjusted composite model toforecast the event in the future period. Thus, where the prior-art failsto recognize and act upon anomalies in time series data, the embodimentrecognizes the anomalies, and provides a methodology that produces moreaccurate forecasts as compared to the prior-art in such anomalousenvironments.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS

The novel features believed characteristic of the invention are setforth in the appended claims. The invention itself, however, as well asa preferred mode of use, further objectives and advantages thereof, willbest be understood by reference to the following detailed description ofthe illustrative embodiments when read in conjunction with theaccompanying drawings, wherein:

FIG. 1 depicts a block diagram of a network of data processing systemsin which illustrative embodiments may be implemented;

FIG. 2 depicts a block diagram of a data processing system in whichillustrative embodiments may be implemented;

FIG. 3 depicts a block diagram of an example application for weightadjusted composite model for forecasting in anomalous environments inaccordance with an illustrative embodiment;

FIG. 4 depicts an example base model combined with an example secondmodel to result in an example composite model in accordance with anillustrative embodiment;

FIG. 5 depicts another example of an anomaly that can be incorporatedinto weight adjusted composite model for forecasting in anomalousenvironments in accordance with an illustrative embodiment;

FIG. 6 depicts another example of an anomaly that can be incorporatedinto weight adjusted composite model for forecasting in anomalousenvironments in accordance with an illustrative embodiment;

FIG. 7 depicts a flowchart of an example process for creating a weightadjustable composite model in accordance with an illustrativeembodiment; and

FIG. 8 depicts a flowchart of an example process for weight adjustedcomposite model for forecasting in anomalous environments in accordancewith an illustrative embodiment.

DETAILED DESCRIPTION

The illustrative embodiments used to describe the invention generallyaddress and solve the above-described problems and other problemsrelated to forecasting events in anomalous time series data. Theillustrative embodiments provide a method, system, and computer programproduct for weight adjusted composite model for forecasting in anomalousenvironments.

An embodiment can be implemented as software instructions of anapplication. The application can be executed on any suitable dataprocessing system.

An embodiment selects a base forecasting model. A base forecasting model(base model) is a forecasting model that is configured to forecastevents when there are no anomalies in the data. In some cases, apre-existing forecasting model can be trained using training data of atime series to forecast events in future data of the time series.

Furthermore, the training data can be but need not necessarily behistorical data of the same time series in which a future event is to bepredicted. For example, an embodiment can be configured such that thebase model uses time series data as it comes in, to train or retrain apreviously existing base model.

Only as an example, and without implying any limitation thereto,consider an example pre-existing base model that conforms to a paraboliccurve with a certain slope and apex values. In other words, the examplepre-existing base model is a quadratic equation with those slope andapex values. Training the base model with some training data can modifythe slope, the apex, or shift when the apex appears to fit an exampleparabolic curve of the training data. Of course, other curves with othercharacteristics and representable as one or more polynomial equations inany degree are similarly usable and trainable as the base model withinthe scope of the illustrative embodiments.

The embodiment identifies an anomaly in the training data. Theembodiment configures a second model so that the second model fits thecurve of the event values in the anomalous portion of the training data.

Only as an example and without implying any limitation thereto, consideran example second model that conforms to a cosine curve. The cosinecurve of the second model may have a fixed frequency, a variablefrequency, a fixed amplitude, a variable amplitude, or some combinationthereof. Configuring the second model to fit the anomaly can modify thefrequency, the amplitude, or a combination thereof, in some or allsegments of the cosine curve. Of course, other curves with othercharacteristics and representable as one or more polynomial equations inany degree are similarly usable and configurable as the second modelwithin the scope of the illustrative embodiments.

Training a base model or configuring a second model in the mannerdescribed above modifies one or more polynomial equations. Themodifications include but are not limited to changing, adding, deleting,or otherwise manipulating a constant in an equation, an exponent in anequation, an operation in an equation, the bounds or range of anequation, a condition in a combination of equations, or some combinationthereof.

An embodiment further combines the trained base model and the configuredsecond model using a mixing algorithm. A mixing algorithm includes butis not limited to a single polynomial equation in any degree, a set ofpolynomial equations in any degrees, a set of one or more constants, aset of one or more conditions, logic, or a combination thereof.Hereinafter, a mixing algorithm is interchangeably referred to as amixing algorithm or a mixing equation, unless expressly distinguishedproximate to where the term is used.

A mixing algorithm manipulates the combination of the trained base modeland the configured second model (hereinafter, “composite model”).Particularly, the mixing algorithm adjusts one or more weights in thecomposite model so that the composite model fits a particular futuresegment of a future anomalous portion in a future data of a given timeseries. A weight in a composite model can be a value of a constant, avalue of an exponent, an operation, a value of a bound or range, a valueof a condition, or some combination thereof. For example, in onesimplified implementation, the mixing algorithm may change a constant ina polynomial equation in the composite model so that a slope of a curvematches a slope of a curve of the anomalous data in a particular segmentof the anomalous data.

An embodiment uses the composite model together with the mixingalgorithm to forecast events in a future time series such that theaccuracy of the forecasted values remain within a threshold variation inthe anomalous as well as non-anomalous portions of the future timeseries. For example, when a forecast of a value of an event is demandedduring a particular segment of an anomalous period in the future timeseries data, the embodiment manipulates the mixing algorithm to changeone or more weights in the composite model so that the weight-adjustedcomposite model achieves a curve that is expected to fit the future dataduring that segment of that anomalous period. The embodiment then usesthe weight-adjusted composite model to forecast a value of the event inthat segment of that anomalous period such that the forecasted valueconforms to the fitted curve.

An embodiment further compares the forecasted value of the event with anactual value of the event as and when the event occurs during thatfuture period. If the forecasted value does not match with the actualvalue within a tolerance, the embodiment retrains the composite model ora part thereof, adjusts the mixing algorithm or a part thereof, or both,so that a second future forecasted value of the event during a secondfuture period is comparatively more likely to conform within thetolerance to the second actual value of the event during that secondfuture period.

A method of an embodiment described herein, when implemented to executeon a device or data processing system, comprises substantial advancementof the functionality of that device or data processing system in eventforecasting in environments where a time series includes anomalous data.For example, where prior-art fails to recognize and act upon anomaliesin time series data, an embodiment recognizes the anomalies, andprovides a methodology that produces more accurate forecasts as comparedto the prior-art in such anomalous environments. Operating in a mannerdescribed herein, an embodiment allows forecasting not only in anomalousportions of data but within segments of those anomalous portions withsignificantly better accuracy than the prior-art. Such manner of eventforecasting in anomalous data is unavailable in presently availabledevices or data processing systems. Thus, a substantial advancement ofsuch devices or data processing systems by executing a method of anembodiment improves the event forecasting capabilities of such devicesor data processing systems while adjusting for anomalies that areobserved in real world events.

The illustrative embodiments are described with respect to certainfunctions, equations, exponents, conditions, curves, values, events,time series data, anomalies, portions, segments, devices, dataprocessing systems, environments, components, and applications only asexamples. Any specific manifestations of these and other similarartifacts are not intended to be limiting to the invention. Any suitablemanifestation of these and other similar artifacts can be selectedwithin the scope of the illustrative embodiments.

Furthermore, the illustrative embodiments may be implemented withrespect to any type of data, data source, or access to a data sourceover a data network. Any type of data storage device may provide thedata to an embodiment of the invention, either locally at a dataprocessing system or over a data network, within the scope of theinvention. Where an embodiment is described using a mobile device, anytype of data storage device suitable for use with the mobile device mayprovide the data to such embodiment, either locally at the mobile deviceor over a data network, within the scope of the illustrativeembodiments.

The illustrative embodiments are described using specific code, designs,architectures, protocols, layouts, schematics, and tools only asexamples and are not limiting to the illustrative embodiments.Furthermore, the illustrative embodiments are described in someinstances using particular software, tools, and data processingenvironments only as an example for the clarity of the description. Theillustrative embodiments may be used in conjunction with othercomparable or similarly purposed structures, systems, applications, orarchitectures. For example, other comparable mobile devices, structures,systems, applications, or architectures therefor, may be used inconjunction with such embodiment of the invention within the scope ofthe invention. An illustrative embodiment may be implemented inhardware, software, or a combination thereof.

The examples in this disclosure are used only for the clarity of thedescription and are not limiting to the illustrative embodiments.Additional data, operations, actions, tasks, activities, andmanipulations will be conceivable from this disclosure and the same arecontemplated within the scope of the illustrative embodiments.

Any advantages listed herein are only examples and are not intended tobe limiting to the illustrative embodiments. Additional or differentadvantages may be realized by specific illustrative embodiments.Furthermore, a particular illustrative embodiment may have some, all, ornone of the advantages listed above.

With reference to the figures and in particular with reference to FIGS.1 and 2, these figures are example diagrams of data processingenvironments in which illustrative embodiments may be implemented. FIGS.1 and 2 are only examples and are not intended to assert or imply anylimitation with regard to the environments in which differentembodiments may be implemented. A particular implementation may makemany modifications to the depicted environments based on the followingdescription.

FIG. 1 depicts a block diagram of a network of data processing systemsin which illustrative embodiments may be implemented. Data processingenvironment 100 is a network of computers in which the illustrativeembodiments may be implemented. Data processing environment 100 includesnetwork 102. Network 102 is the medium used to provide communicationslinks between various devices and computers connected together withindata processing environment 100. Network 102 may include connections,such as wire, wireless communication links, or fiber optic cables.

Clients or servers are only example roles of certain data processingsystems connected to network 102 and are not intended to exclude otherconfigurations or roles for these data processing systems. Server 104and server 106 couple to network 102 along with storage unit 108.Software applications may execute on any computer in data processingenvironment 100. Clients 110, 112, and 114 are also coupled to network102. A data processing system, such as server 104 or 106, or client 110,112, or 114 may contain data and may have software applications orsoftware tools executing thereon.

Only as an example, and without implying any limitation to sucharchitecture, FIG. 1 depicts certain components that are usable in anexample implementation of an embodiment. For example, servers 104 and106, and clients 110, 112, 114, are depicted as servers and clients onlyas example and not to imply a limitation to a client-serverarchitecture. As another example, an embodiment can be distributedacross several data processing systems and a data network as shown,whereas another embodiment can be implemented on a single dataprocessing system within the scope of the illustrative embodiments. Dataprocessing systems 104, 106, 110, 112, and 114 also represent examplenodes in a cluster, partitions, and other configurations suitable forimplementing an embodiment.

Device 132 is an example of a device usable with an embodiment describedherein. For example, device 132 can take the form of a smartphone, atablet computer, a laptop computer, client 110 in a stationary or aportable form, a wearable computing device, or any other suitable devicethat can be configured for requesting entity reviews and analysisreports. Application 105 implements an embodiment described herein.Models 111 forms a repository of models, from which application 105selects a pre-existing base model, and a second model. Application 105trains a base model in models 111, to form a trained base model, usingtraining data 109. Any number and types of data sources, such as datasource 134 and data source 113, can supply one or more time series thatare usable in an embodiment implemented in application 105.

Servers 104 and 106, storage unit 108, and clients 110, 112, and 114 maycouple to network 102 using wired connections, wireless communicationprotocols, or other suitable data connectivity. Clients 110, 112, and114 may be, for example, personal computers or network computers.

In the depicted example, server 104 may provide data, such as bootfiles, operating system images, and applications to clients 110, 112,and 114. Clients 110, 112, and 114 may be clients to server 104 in thisexample. Clients 110, 112, 114, or some combination thereof, may includetheir own data, boot files, operating system images, and applications.Data processing environment 100 may include additional servers, clients,and other devices that are not shown.

In the depicted example, data processing environment 100 may be theInternet. Network 102 may represent a collection of networks andgateways that use the Transmission Control Protocol/Internet Protocol(TCP/IP) and other protocols to communicate with one another. At theheart of the Internet is a backbone of data communication links betweenmajor nodes or host computers, including thousands of commercial,governmental, educational, and other computer systems that route dataand messages. Of course, data processing environment 100 also may beimplemented as a number of different types of networks, such as forexample, an intranet, a local area network (LAN), or a wide area network(WAN). FIG. 1 is intended as an example, and not as an architecturallimitation for the different illustrative embodiments.

Among other uses, data processing environment 100 may be used forimplementing a client-server environment in which the illustrativeembodiments may be implemented. A client-server environment enablessoftware applications and data to be distributed across a network suchthat an application functions by using the interactivity between aclient data processing system and a server data processing system. Dataprocessing environment 100 may also employ a service orientedarchitecture where interoperable software components distributed acrossa network may be packaged together as coherent business applications.

With reference to FIG. 2, this figure depicts a block diagram of a dataprocessing system in which illustrative embodiments may be implemented.Data processing system 200 is an example of a computer, such as servers104 and 106, or clients 110, 112, and 114 in FIG. 1, or another type ofdevice in which computer usable program code or instructionsimplementing the processes may be located for the illustrativeembodiments.

Data processing system 200 is also representative of a data processingsystem or a configuration therein, such as data processing system 132 inFIG. 1 in which computer usable program code or instructionsimplementing the processes of the illustrative embodiments may belocated. Data processing system 200 is described as a computer only asan example, without being limited thereto. Implementations in the formof other devices, such as device 132 in FIG. 1, may modify dataprocessing system 200, modify data processing system 200, such as byadding a touch interface, and even eliminate certain depicted componentsfrom data processing system 200 without departing from the generaldescription of the operations and functions of data processing system200 described herein.

In the depicted example, data processing system 200 employs a hubarchitecture including North Bridge and memory controller hub (NB/MCH)202 and South Bridge and input/output (I/O) controller hub (SB/ICH) 204.Processing unit 206, main memory 208, and graphics processor 210 arecoupled to North Bridge and memory controller hub (NB/MCH) 202.Processing unit 206 may contain one or more processors and may beimplemented using one or more heterogeneous processor systems.Processing unit 206 may be a multi-core processor. Graphics processor210 may be coupled to NB/MCH 202 through an accelerated graphics port(AGP) in certain implementations.

In the depicted example, local area network (LAN) adapter 212 is coupledto South Bridge and I/O controller hub (SB/ICH) 204. Audio adapter 216,keyboard and mouse adapter 220, modem 222, read only memory (ROM) 224,universal serial bus (USB) and other ports 232, and PCI/PCIe devices 234are coupled to South Bridge and I/O controller hub 204 through bus 238.Hard disk drive (HDD) or solid-state drive (SSD) 226 and CD-ROM 230 arecoupled to South Bridge and I/O controller hub 204 through bus 240.PCI/PCIe devices 234 may include, for example, Ethernet adapters, add-incards, and PC cards for notebook computers. PCI uses a card buscontroller, while PCIe does not. ROM 224 may be, for example, a flashbinary input/output system (BIOS). Hard disk drive 226 and CD-ROM 230may use, for example, an integrated drive electronics (IDE), serialadvanced technology attachment (SATA) interface, or variants such asexternal-SATA (eSATA) and micro-SATA (mSATA). A super I/O (SIO) device236 may be coupled to South Bridge and I/O controller hub (SB/ICH) 204through bus 238.

Memories, such as main memory 208, ROM 224, or flash memory (not shown),are some examples of computer usable storage devices. Hard disk drive orsolid state drive 226, CD-ROM 230, and other similarly usable devicesare some examples of computer usable storage devices including acomputer usable storage medium.

An operating system runs on processing unit 206. The operating systemcoordinates and provides control of various components within dataprocessing system 200 in FIG. 2. The operating system may be acommercially available operating system such as AIX® (AIX is a trademarkof International Business Machines Corporation in the United States andother countries), Microsoft® Windows® (Microsoft and Windows aretrademarks of Microsoft Corporation in the United States and othercountries), Linux® (Linux is a trademark of Linus Torvalds in the UnitedStates and other countries), iOS™ (iOS is a trademark of Cisco Systems,Inc. licensed to Apple Inc. in the United States and in othercountries), or Android™ (Android is a trademark of Google Inc., in theUnited States and in other countries). An object oriented programmingsystem, such as the Java™ programming system, may run in conjunctionwith the operating system and provide calls to the operating system fromJava™ programs or applications executing on data processing system 200(Java and all Java-based trademarks and logos are trademarks orregistered trademarks of Oracle Corporation and/or its affiliates).

Instructions for the operating system, the object-oriented programmingsystem, and applications or programs, such as application 105 in FIG. 1,are located on storage devices, such as hard disk drive 226, and may beloaded into at least one of one or more memories, such as main memory208, for execution by processing unit 206. The processes of theillustrative embodiments may be performed by processing unit 206 usingcomputer implemented instructions, which may be located in a memory,such as, for example, main memory 208, read only memory 224, or in oneor more peripheral devices.

The hardware in FIGS. 1-2 may vary depending on the implementation.Other internal hardware or peripheral devices, such as flash memory,equivalent non-volatile memory, or optical disk drives and the like, maybe used in addition to or in place of the hardware depicted in FIGS.1-2. In addition, the processes of the illustrative embodiments may beapplied to a multiprocessor data processing system.

In some illustrative examples, data processing system 200 may be apersonal digital assistant (PDA), which is generally configured withflash memory to provide non-volatile memory for storing operating systemfiles and/or user-generated data. A bus system may comprise one or morebuses, such as a system bus, an I/O bus, and a PCI bus. Of course, thebus system may be implemented using any type of communications fabric orarchitecture that provides for a transfer of data between differentcomponents or devices attached to the fabric or architecture.

A communications unit may include one or more devices used to transmitand receive data, such as a modem or a network adapter. A memory may be,for example, main memory 208 or a cache, such as the cache found inNorth Bridge and memory controller hub 202. A processing unit mayinclude one or more processors or CPUs.

The depicted examples in FIGS. 1-2 and above-described examples are notmeant to imply architectural limitations. For example, data processingsystem 200 also may be a tablet computer, laptop computer, or telephonedevice in addition to taking the form of a mobile or wearable device.

With reference to FIG. 3, this figure depicts a block diagram of anexample application for weight adjusted composite model for forecastingin anomalous environments in accordance with an illustrative embodiment.Application 302 is an example of application 105 in FIG. 3. Inimplementation, application 302 can be reconfigured into similarlypurposed but differently configured more than one application withwithout departing the scope of the illustrative embodiments.

Component 304 selects a base model, e.g., from models 111 in FIG. 1.Component 304 trains the selected base model, e.g., using training data109 in FIG. 1, so that the trained base model fits at least thenon-anomalous portions of the training data.

Component 306 performs anomaly modeling. For example, component 306identifies an anomalous portion of the training data. Component 306selects a suitable second model that can be configured to fit theanomalous portion.

Note that there is no limitation on the number or types of anomaliesthat can exist in a given time series. Accordingly, when component 306identifies more than one anomalous portion, component 306 may select oneor more second models to differently configure and fit differentanomalous portions.

Component 308 combines the trained base model and the configured one ormore second models to form a composite model. Component 310 furthercombines a mixing algorithm with the composite model. Component 310configures the mixing algorithm such that the mixing algorithm can bemanipulated to perform weight adjustments in the combined algorithm.

Component 312 performs event forecasting using the composite model andthe mixing algorithm. The forecasting of an event during a future periodby component 312 conforms to the anomalies expected in the data duringthat future period, or a segment thereof. For example, to forecast anevent in a segment of a future anomalous period in a time series,component 312 adjusts one or more weights in the composite model so thatthe resulting composite model curve fits the curve of the training timeseries data in a similar segment of a similar anomalous period that haspassed.

With reference to FIG. 4, this figure depicts an example base modelcombined with an example second model to result in an example compositemodel in accordance with an illustrative embodiment. Base model 402 isselected and trained using component 304 or a similarly purposedequivalent thereof, to fit an example parabolic curve as shown.

Second model 404 is selected and configured using component 306 or asimilarly purposed equivalent thereof, to fit an example cosine curve asshown. Seasonal variations in a factor affecting an event can producesuch anomalies in a time series. Composite model 406 results fromcomponent 308 combining models 402 and 404.

Assume that model 406 is suitably weighted using an associated mixingalgorithm for the following example. Suppose that a forecast using onlymodel 402 forecasts the event value 402A as shown on the graph of model402. At point 402A, the model yields a Y value of approximately 1 on thedepicted scale.

Now consider two example scenarios—first, where point 404A lies in afirst segment S1 of an anomalous period P, and second, where point 404Blies in a second segment S2 of the anomalous period P.

Composite model 406 shows that event value 406A during segment S1, andparticularly at point 404A, is approximately zero, not approximately 1as base model 402 would forecast. Similarly, composite model 406 showsthat event value 406B during segment S2, and particularly at point 404B,is approximately 2, not approximately 1 as base model 402 wouldforecast.

As can be seen in this simplified example, the forecasted value of anevent is dependent upon the anomalies that are expected to arise duringthe particular time or time segment of a future period. Therefore, theaccuracy of the forecasted value is more accurate when such anomaliesare considered in a weight adjusted composite model according to theillustrative embodiments.

With reference to FIG. 5, this figure depicts another example of ananomaly that can be incorporated into weight adjusted composite modelfor forecasting in anomalous environments in accordance with anillustrative embodiment. Second model 504 is usable in place of, or inaddition to, second model 404 in FIG. 4.

Second model 504 can be selected and configured using component 306 or asimilarly purposed equivalent thereof, to fit an example level curve asshown. A change in a level of a factor affecting an event can producesuch level-type anomalies in a time series.

Combining second model 504 with base model 402 in FIG. 4 would yield acomposite model (not shown) that is different from composite model 406.If the forecasted event is to appear during period P on the curve ofsecond model 504, the level anomalies in a weight adjusted compositemodel (not shown) according to the illustrative embodiments would yielda more accurate value of the event as compared to just base model 402.

With reference to FIG. 6, this figure depicts another example of ananomaly that can be incorporated into weight adjusted composite modelfor forecasting in anomalous environments in accordance with anillustrative embodiment. Second model 604 is usable in place of, or inaddition to, second model 404 in FIG. 4 and/or second model 504 in FIG.5.

Second model 604 can be selected and configured using component 306 or asimilarly purposed equivalent thereof, to fit an example trend curve asshown. A change in a trend of a factor affecting an event can producesuch trend-type anomalies in a time series.

Combining second model 604 with base model 402 in FIG. 4 would yield acomposite model (not shown) that is different from composite model 406.If the forecasted event is to appear during period P on the curve ofsecond model 604, the level anomalies in a weight adjusted compositemodel (not shown) according to the illustrative embodiments would yielda more accurate value of the event as compared to just base model 402.

With reference to FIG. 7, this figure depicts a flowchart of an exampleprocess for creating a weight adjustable composite model in accordancewith an illustrative embodiment. Process 700 an be implemented inapplication 302 in FIG. 3, to produce a weigh adjustable compositemodel, for example, composite model 406 in FIG. 4.

The application selects a base model (bloc 702). The applicationidentifies an anomaly in the training data for the selected base model(block 704). The application configures a second model to fit theanomaly block 706). The application combined the trained base model andthe configured second model using a mixing algorithm for weightadjustments (block 708). The application ends process 700 thereafter.

With reference to FIG. 8, this figure depicts a flowchart of an exampleprocess for weight adjusted composite model for forecasting in anomalousenvironments in accordance with an illustrative embodiment. Process 800can be implemented in application 302 in FIG. 3.

The application identifies a future period or a segment thereof duringwhich an event has to be forecasted (block 802). The applicationdetermines a portion of a curve in a configured second model that isrepresentative of the future period or the segment thereof (block 804).For example, the application identifies a period or a segment at leastone of whose characteristics is similar to a correspondingcharacteristic of the future period or segment.

For example, if the future segment occurs between 2 and 3 PM, theapplication identifies a curve section that corresponds to the 2-3 PMtime segment. Any suitable characteristic of the forecasting period orsegment is similarly usable within the scope of the illustrativeembodiments. A non-limiting and non-exhaustive list of somecharacteristics usable in this manner include a weather characteristicat that time, a traffic characteristic at that time, a skill of a personoperating in that time, a factor affecting the event at that time, andthe like.

The application adjusts one or more weights in the composite model usingthe mixing algorithm according to the one or more characteristics of thefuture period or segment during which the event is to be forecasted(block 806). The application executes the weight adjusted compositemodel to forecast a value of the event during the future period or timesegment (block 808). The application ends process 800 thereafter.

Thus, a computer implemented method, system or apparatus, and computerprogram product are provided in the illustrative embodiments for weightadjusted composite model for forecasting in anomalous environments.Where an embodiment or a portion thereof is described with respect to atype of device, the computer implemented method, system or apparatus,the computer program product, or a portion thereof, are adapted orconfigured for use with a suitable and comparable manifestation of thattype of device.

The present invention may be a system, a method, and/or a computerprogram product. The computer program product may include a computerreadable storage medium (or media) having computer readable programinstructions thereon for causing a processor to carry out aspects of thepresent invention.

The computer readable storage medium can be a tangible device that canretain and store instructions for use by an instruction executiondevice. The computer readable storage medium may be, for example, but isnot limited to, an electronic storage device, a magnetic storage device,an optical storage device, an electromagnetic storage device, asemiconductor storage device, or any suitable combination of theforegoing. A non-exhaustive list of more specific examples of thecomputer readable storage medium includes the following: a portablecomputer diskette, a hard disk, a random access memory (RAM), aread-only memory (ROM), an erasable programmable read-only memory (EPROMor Flash memory), a static random access memory (SRAM), a portablecompact disc read-only memory (CD-ROM), a digital versatile disk (DVD),a memory stick, a floppy disk, a mechanically encoded device such aspunch-cards or raised structures in a groove having instructionsrecorded thereon, and any suitable combination of the foregoing. Acomputer readable storage medium, as used herein, is not to be construedas being transitory signals per se, such as radio waves or other freelypropagating electromagnetic waves, electromagnetic waves propagatingthrough a waveguide or other transmission media (e.g., light pulsespassing through a fiber-optic cable), or electrical signals transmittedthrough a wire.

Computer readable program instructions described herein can bedownloaded to respective computing/processing devices from a computerreadable storage medium or to an external computer or external storagedevice via a network, for example, the Internet, a local area network, awide area network and/or a wireless network. The network may comprisecopper transmission cables, optical transmission fibers, wirelesstransmission, routers, firewalls, switches, gateway computers and/oredge servers. A network adapter card or network interface in eachcomputing/processing device receives computer readable programinstructions from the network and forwards the computer readable programinstructions for storage in a computer readable storage medium withinthe respective computing/processing device.

Computer readable program instructions for carrying out operations ofthe present invention may be assembler instructions,instruction-set-architecture (ISA) instructions, machine instructions,machine dependent instructions, microcode, firmware instructions,state-setting data, or either source code or object code written in anycombination of one or more programming languages, including an objectoriented programming language such as Smalltalk, C++ or the like, andconventional procedural programming languages, such as the “C”programming language or similar programming languages. The computerreadable program instructions may execute entirely on the user'scomputer, partly on the user's computer, as a stand-alone softwarepackage, partly on the user's computer and partly on a remote computeror entirely on the remote computer or server. In the latter scenario,the remote computer may be connected to the user's computer through anytype of network, including a local area network (LAN) or a wide areanetwork (WAN), or the connection may be made to an external computer(for example, through the Internet using an Internet Service Provider).In some embodiments, electronic circuitry including, for example,programmable logic circuitry, field-programmable gate arrays (FPGA), orprogrammable logic arrays (PLA) may execute the computer readableprogram instructions by utilizing state information of the computerreadable program instructions to personalize the electronic circuitry,in order to perform aspects of the present invention.

Aspects of the present invention are described herein with reference toflowchart illustrations and/or block diagrams of methods, apparatus(systems), and computer program products according to embodiments of theinvention. It will be understood that each block of the flowchartillustrations and/or block diagrams, and combinations of blocks in theflowchart illustrations and/or block diagrams, can be implemented bycomputer readable program instructions.

These computer readable program instructions may be provided to aprocessor of a general purpose computer, special purpose computer, orother programmable data processing apparatus to produce a machine, suchthat the instructions, which execute via the processor of the computeror other programmable data processing apparatus, create means forimplementing the functions/acts specified in the flowchart and/or blockdiagram block or blocks. These computer readable program instructionsmay also be stored in a computer readable storage medium that can directa computer, a programmable data processing apparatus, and/or otherdevices to function in a particular manner, such that the computerreadable storage medium having instructions stored therein comprises anarticle of manufacture including instructions which implement aspects ofthe function/act specified in the flowchart and/or block diagram blockor blocks.

The computer readable program instructions may also be loaded onto acomputer, other programmable data processing apparatus, or other deviceto cause a series of operational steps to be performed on the computer,other programmable apparatus or other device to produce a computerimplemented process, such that the instructions which execute on thecomputer, other programmable apparatus, or other device implement thefunctions/acts specified in the flowchart and/or block diagram block orblocks.

The flowchart and block diagrams in the Figures illustrate thearchitecture, functionality, and operation of possible implementationsof systems, methods, and computer program products according to variousembodiments of the present invention. In this regard, each block in theflowchart or block diagrams may represent a module, segment, or portionof instructions, which comprises one or more executable instructions forimplementing the specified logical function(s). In some alternativeimplementations, the functions noted in the block may occur out of theorder noted in the figures. For example, two blocks shown in successionmay, in fact, be executed substantially concurrently, or the blocks maysometimes be executed in the reverse order, depending upon thefunctionality involved. It will also be noted that each block of theblock diagrams and/or flowchart illustration, and combinations of blocksin the block diagrams and/or flowchart illustration, can be implementedby special purpose hardware-based systems that perform the specifiedfunctions or acts or carry out combinations of special purpose hardwareand computer instructions.

What is claimed is:
 1. A method for event forecasting in anomalousenvironments, the method comprising: combining with a base forecastingmodel a second forecasting model to form a composite model, the baseforecasting model configured to forecast an event in a time series, thesecond forecasting model configured to represent an anomalous portion ofdata in the time series; combining with the composite model a mixingalgorithm, the mixing algorithm configured to adjust a set of weightsassociated with the composite model; adjusting, responsive toidentifying a future period in which the event is to be forecasted,using the mixing algorithm, a subset of the set of weights to from aweight adjusted composite model; and executing, using a processor and amemory, the weight adjusted composite model to forecast the event in thefuture period.
 2. The method of claim 1, further comprising: identifyinga characteristic of the future period; identifying a second period in atraining data, wherein the characteristic of the future period matches acorresponding characteristic of the second period within a threshold;and determining a portion of a curve representing a set of anomalousvalues in the training data during the second period, wherein theadjusting matches a curve representing the composite model during thefuture period with the portion of the curve representing the set ofanomalous values in the training data during the second period.
 3. Themethod of claim 2, wherein the training data comprises past data of thetime series.
 4. The method of claim 2, wherein the characteristiccomprises a factor that affects the event during the future period. 5.The method of claim 2, wherein the characteristic comprises a time ofday.
 6. The method of claim 1, wherein the second forecasting modelcomprises an equation whose curve fits, within a threshold, a curveformed by a set of values in the anomalous portion, and wherein the baseforecasting model forecasts a value of the event in a non-anomalousportion of the data of the time series.
 7. The method of claim 1,further comprising: configuring the set of weights in the compositemodel, wherein a weight in the set of weights is associated with anexpression in an equation in the composite model, wherein adjusting theweight causes a curve of the equation to change and form a changedcurve, and wherein the changed fits, within a threshold, a second curveformed by a set of values in an expected anomalous portion in the timeseries during the future period.
 8. The method of claim 1, wherein thesecond forecasting model comprises an equation representing a seasonalchange in the time series.
 9. The method of claim 1, wherein the secondforecasting model comprises an equation representing a level change inthe time series.
 10. The method of claim 1, wherein the secondforecasting model comprises an equation representing a trend change inthe time series.
 11. The method of claim 1, wherein the method isembodied in a computer program product comprising one or morecomputer-readable tangible storage devices and computer-readable programinstructions which are stored on the one or more computer-readabletangible storage devices and executed by one or more processors.
 12. Themethod of claim 1, wherein the method is embodied in a computer systemcomprising one or more processors, one or more computer-readablememories, one or more computer-readable tangible storage devices andprogram instructions which are stored on the one or morecomputer-readable tangible storage devices for execution by the one ormore processors via the one or more memories and executed by the one ormore processors.
 13. A computer program product for event forecasting inanomalous environments, the computer program product comprising: one ormore computer-readable tangible storage devices; program instructions,stored on at least one of the one or more storage devices, to combinewith a base forecasting model a second forecasting model to form acomposite model, the base forecasting model configured to forecast anevent in a time series, the second forecasting model configured torepresent an anomalous portion of data in the time series; programinstructions, stored on at least one of the one or more storage devices,to combine with the composite model a mixing algorithm, the mixingalgorithm configured to adjust a set of weights associated with thecomposite model; program instructions, stored on at least one of the oneor more storage devices, to adjust, responsive to identifying a futureperiod in which the event is to be forecasted, using the mixingalgorithm, a subset of the set of weights to from a weight adjustedcomposite model; and program instructions, stored on at least one of theone or more storage devices, to execute, using a processor and a memory,the weight adjusted composite model to forecast the event in the futureperiod.
 14. The computer program product of claim 13, furthercomprising: program instructions, stored on at least one of the one ormore storage devices, to identify a characteristic of the future period;program instructions, stored on at least one of the one or more storagedevices, to identify a second period in a training data, wherein thecharacteristic of the future period matches a correspondingcharacteristic of the second period within a threshold; and programinstructions, stored on at least one of the one or more storage devices,to determine a portion of a curve representing a set of anomalous valuesin the training data during the second period, wherein the adjustingmatches a curve representing the composite model during the futureperiod with the portion of the curve representing the set of anomalousvalues in the training data during the second period.
 15. The computerprogram product of claim 14, wherein the training data comprises pastdata of the time series.
 16. The computer program product of claim 14,wherein the characteristic comprises a factor that affects the eventduring the future period.
 17. The computer program product of claim 14,wherein the characteristic comprises a time of day.
 18. The computerprogram product of claim 13, wherein the second forecasting modelcomprises an equation whose curve fits, within a threshold, a curveformed by a set of values in the anomalous portion, and wherein the baseforecasting model forecasts a value of the event in a non-anomalousportion of the data of the time series.
 19. The computer program productof claim 13, further comprising: program instructions, stored on atleast one of the one or more storage devices, to configure the set ofweights in the composite model, wherein a weight in the set of weightsis associated with an expression in an equation in the composite model,wherein adjusting the weight causes a curve of the equation to changeand form a changed curve, and wherein the changed fits, within athreshold, a second curve formed by a set of values in an expectedanomalous portion in the time series during the future period.
 20. Acomputer system for event forecasting in anomalous environments, thecomputer system comprising: one or more processors, one or morecomputer-readable memories and one or more computer-readable storagedevices; program instructions, stored on at least one of the one or morestorage devices for execution by at least one of the one or moreprocessors via at least one of the one or more memories, to combine witha base forecasting model a second forecasting model to form a compositemodel, the base forecasting model configured to forecast an event in atime series, the second forecasting model configured to represent ananomalous portion of data in the time series; program instructions,stored on at least one of the one or more storage devices for executionby at least one of the one or more processors via at least one of theone or more memories, to combine with the composite model a mixingalgorithm, the mixing algorithm configured to adjust a set of weightsassociated with the composite model; program instructions, stored on atleast one of the one or more storage devices for execution by at leastone of the one or more processors via at least one of the one or morememories, to adjust, responsive to identifying a future period in whichthe event is to be forecasted, using the mixing algorithm, a subset ofthe set of weights to from a weight adjusted composite model; andprogram instructions, stored on at least one of the one or more storagedevices for execution by at least one of the one or more processors viaat least one of the one or more memories, to execute, using a processorand a memory, the weight adjusted composite model to forecast the eventin the future period.